For the sake of simplicity, we take the \(t\) -th frame compression as an example to explain the P-frame compression process without considering I-frame compression.
\(\hat{y}_t\)  and \(\hat{y}_{t-1}\)  are generated from input frames (\(x_{t}\)  and \(x_{t-1}\) ) by the fixed Encoder network, downsampling with 16x size scaling.
To further reduce the information entropy, we use the differential \(\hat{y}_{t_{res}}\)  between \(\hat{y}_t\)  and \(\hat{y}_{t-1}\)  as the input of AE.
To enable more accurate probability distribution, the temporal compaction is conducted using three prior modules (e.g., hyper-prior Encoder-Decoder, spatial prior module, and temporal prior module) with \(\hat{y}_t\)  and \(\hat{y}_{t-1}\)  as inputs.
The P-HE network takes \(\hat{y}_t\)  and \(\hat{y}_{t-1}\)  as inputs to generate the hyper latent \(\hat{z}_{t}\) , the SPM network uses PixelCNN structure [1]} to capture the spatial priors between the neighbors in \(\hat{y}_{t_{res}}\) , and the TPM network uses three convolutions with Leaky ReLU to extract temporal priors from the previous latent \(\hat{y}_{t-1}\) .
To generate the probability distribution parameters \(({\mu _t}, {\sigma _t})\) , the EPM module is introduced to fuse the outputs of P-HD, SPM and TPM.
Similar to [2]}, the probability \(p_{\hat{y}}(\hat{y})\)  of quantized latent \({\hat{y}}\)  is modeled as Laplacian distribution:
\(p_{\hat{y}_{t_{res}}}(\hat{y}_{t_{res}}|{\hat{y}_{t-1}}, {\hat{z}_{t}})=\prod _{i=1}\Big (\int _{{\hat{y}_i}-\frac{1}{2}}^{{\hat{y}_i}+\frac{1}{2}} Lap({\hat{y}_{t_{res}}};\mu _t, e^{\sigma _t})\, dy\Big ).\) 
